摘要
高阶边界元法在很多工程计算中得到了广泛的应用,但由于需要多次求解格林函数及其导数,高昂的计算量和存储量使其很难应用于大型工程问题。本文采用快速多极子方法,对于形如l/r的简单格林函数采用球坐标系下的双谐展开,对于满足自由水面条件的复杂格林函数则在柱坐标系下展开,使其计算量和存储量都由未知量的平方量级降为未知量的线性量级。对于高阶边界元法中的固角系数和柯西主值积分本文采用了直接求解的方法。通过对无限区域中水流对圆球的绕射和波浪与漂浮方箱的数值计算,表明对于大中型计算问题FMM算法更加有效。
The higher order boundary element method （HOBEM） has been widely used in engineering calculations, but it is difficult to solve the large-scale problems because of large computation cost and computer storage needed to compute the Green＇s function and its＇ corresponding derivatives many times.In this paper,the fast multipole method is applied in HOBEM to overcome the embarrassing situation.The simple Green＇s function （l/r） and the Green＇s function satisfying the free surface boundary conditions are expanded in sphere coordinate and the cylinder coordinate system respectively,which can result in the computation cost and computer storage being decreased from O（N^2） order to nearly O（N） order.The free-term coefficient and the CPV integrals are obtained by using a direct method in higher-order boundary integral equation.In order to verify this present numerical model,the flow diffraction from a stationary sphere in an unbounded domain and wave actions on a floating box are simulated respectively.The results show that this present method is accurate enough and more efficient to solve the large-scale problems.
关键词
高阶边界元法
快速多极子方法
格林函数
higher order boundary element method
fast multipole method
Green＇s function
